2y^2+6y-1=0

Simple and best practice solution for 2y^2+6y-1=0 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for 2y^2+6y-1=0 equation:


Simplifying
2y2 + 6y + -1 = 0

Reorder the terms:
-1 + 6y + 2y2 = 0

Solving
-1 + 6y + 2y2 = 0

Solving for variable 'y'.

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-0.5 + 3y + y2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 3y + 0.5 + y2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 3y + y2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 3y + y2 = 0 + 0.5
3y + y2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
3y + y2 = 0.5

The y term is 3y.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3y + 2.25 + y2 = 0.5 + 2.25

Reorder the terms:
2.25 + 3y + y2 = 0.5 + 2.25

Combine like terms: 0.5 + 2.25 = 2.75
2.25 + 3y + y2 = 2.75

Factor a perfect square on the left side:
(y + 1.5)(y + 1.5) = 2.75

Calculate the square root of the right side: 1.658312395

Break this problem into two subproblems by setting 
(y + 1.5) equal to 1.658312395 and -1.658312395.

Subproblem 1

y + 1.5 = 1.658312395 Simplifying y + 1.5 = 1.658312395 Reorder the terms: 1.5 + y = 1.658312395 Solving 1.5 + y = 1.658312395 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + y = 1.658312395 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = 1.658312395 + -1.5 y = 1.658312395 + -1.5 Combine like terms: 1.658312395 + -1.5 = 0.158312395 y = 0.158312395 Simplifying y = 0.158312395

Subproblem 2

y + 1.5 = -1.658312395 Simplifying y + 1.5 = -1.658312395 Reorder the terms: 1.5 + y = -1.658312395 Solving 1.5 + y = -1.658312395 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + y = -1.658312395 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = -1.658312395 + -1.5 y = -1.658312395 + -1.5 Combine like terms: -1.658312395 + -1.5 = -3.158312395 y = -3.158312395 Simplifying y = -3.158312395

Solution

The solution to the problem is based on the solutions from the subproblems. y = {0.158312395, -3.158312395}

See similar equations:

| 10x-4(x-2)=12x+7(x+3) | | 30=9x+2-2x | | 12x^2+18x+4=0 | | -8x-5=91 | | -17=7+6x | | 12x+8x=180 | | 0.10x+.05(14-x)=.10(16) | | 8(8x+7)-2=-2(x+6) | | -25-7m=20m-25 | | Z=1+0.75x | | F+9-n= | | 80x+40=80x-4 | | 2z^2+3z+1=0 | | -x^3+5x^2+50x=0 | | 7x-4+4x+4=110 | | 8x+(6)= | | 2n-3=5+6n+8n-8 | | 11x-3=8x+11 | | 3(y-21)+2(y-2)=13 | | 7x+3(6x-15)=-170 | | 58-11x=12+12x | | 2y=-16x+36 | | R=4+7-sx | | 7x-4=4x+4 | | 4(m-2)=-2(m+3) | | 3(x-23)+3(x-2)=33 | | 6(x+1)=2(3x-4) | | 3.4+10m=7.92 | | 3(-2-3f)=-9f-4 | | 5(x-3)-2(x-7)=-7(2x-5) | | -15y+30-y=-3y+12 | | -16t^2+96t+12= |

Equations solver categories